For All Intensive Purposes

You can look through the articles' examples at https://specialessays.com/buy-book-reports/ for a chance to buy book report of a good quality.

As for the question in the title, I don't know. And I'm not even going to try to answer that question (you can read what the FDA says); however, there are two statements that every scientist can agree upon. 

1. Microwave radiation is non-ionizing. (Both cell phones and microwave ovens emit microwaves). That means that the energy of a single microwave is far too weak to break electrical bonds. Ionizing radiation can cause cancer by causing DNA to mutate.
2. Cell phones and microwave ovens emit a lot of radiation. They both emit a lot of individual microwaves. Microwave ovens are shielded, however, and very little radiation should be able to escape. Cell phones on the other hand emit less radiation; however, since your cell phone has no idea where the nearest cell tower is, the phone emits the same radiation in all directions, including right through your head (cell phones can judge distance, but not direction).
   

This post will attempt to quantitatively compare the radiation leaked from microwave ovens (and how well they're shielded) to the radiation emitted from cell phones.

Microwave Ovens
In the wrong hands, microwave ovens can become weapons of mass destruction (see above).

Consumer ovens typically operate at 2.45 GHz and apparently must comply with some FDA regulations (actually, they have to comply with all of section J (parts 1000-1050)). The regulations are largely boring, incomprehensible, and irrelevant to this post; however, paragraph (c)(1) addresses the issue of radiation leakage:

Power density limit. The equivalent plane-wave power density existing in the proximity of the external oven surface shall not exceed 1 milliwatt per square centimeter at any point 5 centimeters or more from the external surface of the oven, measured prior to acquisition by a purchaser, and, thereafter, 5 milliwatts per square centimeter at any such point.

(FCC Sec. 1.1310 limits the maximum permissible exposure (MPE) of non-portable devices. For the general public, the MPE for frequencies greater than 1.5 GHz is 1 mW/cm sq for 30 minutes; for occupation/controlled exposure, the MPE over the same frequency range is 5 mW/cm sq).

The microwave oven under consideration (see photo above) has outer dimensions of 56x30.5x39.5 cm. The area of a surface that surrounds every point of the oven at a distance of 5 cm is approximately 10500 cm sq. This particular oven has an IEC 60705 standard rating of 1200 W (the rating is acquired through calorimetry; for debatably interesting information about oven power output, click here or here). If the oven was unshielded, the power density at 5 cm would average to 114 mW/cm sq. I'll talk more about shielding later.

Comparing the DHHS regulation with the above calculation is a bit tricky. The regulation is specific to a particular point; it's presumable unlikely that a microwave oven will leak evenly in all directions. With that caveat, if an oven complies with DHHS regulations, it will leak no more than about 4.4% at a particular point.

Cell Phones
Cell phones operate between .85 and 1.9 GHz, depending on location (you can find your cell phone's frequency here (you can also look at this really confusing NTIA chart)). Cell phones continuously adjust and minimize RF power while operating to decrease interference at cell towers; the outputted power depends on many things including terrain and distance to the nearest tower. Phones on a GSM network (80% worldwide are) use 8 channel TDMA communication; this means that a cell phone would only transmit 1/8 of the time (all cell phone powers quoted in this bloq will be averaged over one full cycle -- to find the peak power, multiply by 8). Several studies (Sweden, US & Some World, and Italy) have measured typical transmission powers; the average US value was 86 mW, although outputs of up to 2 W with a .9 GHz phone were measured in rural areas in Sweden.

Because cell phones are portable, FCC Sec. 1.1310 does not apply. (Parenthetically, I'd say regulating portability is a practicality issue). If it did, a 86 mW phone (with frequency greater than 1.5 GHz) would need to be held 2.6 cm from your body; a 2 W, .9 GHz phone (the MPE at .9 GHz is .6 mW/cm sq) would need to be held 16 cm away! (I've calcutated these limits using the general public limits (3o minutes exposure); for occupational use (6 minutes of exposure), the distances are about half).

Fortunately, FCC Sec 2.1093 addresses portable devices. Unfortunately, they address the issue with a complicated unit, the SAR (specific absorption rate), which for the general population is 0.08 W/kg averaged over the whole body or 1.6 W/kg over a 1 g tissue cube (in Europe, the limit is 2 W/kg averaged over 10 g of tissue). You can find your cell phones tissue rated SAR here. The SAR takes into account the electrical conductivity of tissue (which is related to how much tissue responds to radiation) and the density (which tells how much radiation the tissue can absorb). Because the conductivity is frequency dependent, a phone will have a different rate depending on its network (.9 GHz or 1.8 GHz, e.g.), which will be different than the SAR from a microwave oven (2.45 GHz).

Comparison
The top plot shows the large distance behavior or the SAR. The shape of the blue curves (microwave oven) is different from the red curves (cell phones) because I've assumed the radiation falls off according to the distance from the oven surface; I've assumed cell phone radiation falls off according to the distance from a point-like antena. From the top plot, it's clear that the long distance behavior of both types of radiation is well below the SAR limit for head exposure (or body exposure).

The bottom plot shows the short distance behavior of the SAR. In this regime, cell phone radiation dominates. In the US, the SAR from the average cell phone is below the acceptable limit of 1.6 W/kg (the distance is measured from antena to head -- the antena is on the side of the phone farthest from your head). In rural Sweden, typical phone calls are carried out very close to the 2 W/kg legal European limit (apparently in rural Sweden it's safer to just yodel (see title of blog)).

Cell Phone in Microwave Oven
Have you ever wondered what would happen if you put your cell phone inside of a microwave oven? (No, not while the oven is on.) Some time ago, I put my cell phone inside my microwave oven. It's hard to see through the wire mesh inside the oven (which is why I don't have a picture of this), but my phone still registered 1 out of 4 bars of reception. This surprised me. I then tried and succeeded in placing a call to my phone while it was in the oven. I was also able to place an already connected cell phone in the microwave and not lose the connection.

Presumably, if a microwave oven is really well shielded, a cell phone shouldn't be able to work inside of it. Since the two frequencies (2.45 GHz for the oven, 1.9 GHz for the cell phone) are very close to each other, the fraction of transmitted radiation (whether from the oven itself or a cell phone inside of an oven) should be very similar. Microwave ovens inhibit microwave radiation transmission because they're surround by a good conductor (steel). So why was I able to get reception?

A good conductor has a shallow skin depth (a shallow skin depth permits very little radiation leakage) given by:
For comparison's sake, none of the above quantities really matter except for f (the frequency). Radiation at 1.9 GHz has a skin depth that is 14% deeper than radiation at 2.45 GHz (at 0.9 GHz, the skin depth is 65% deeper than 2.45 GHz). This means that it's easier for lower frequency radiation to leak from inside (or outside) of a microwave oven.

The fractional intensity of transmitted radiation is given by:
where z is the thickness of the oven. Assuming the oven is made out of stainless steel (the conductivity of SS304 is approximately 1.5x10^6 /ohm-m) and that the oven complies with FCC regulations, the thickness of the metal shielding can be approximated to 0.036mm prior to purchase (0.024mm thereafter). Since the metal frame of the oven is clearly thicker than this, these numbers must refer to the effective thickness of the glass window. The glass window has a wire mesh (faraday cage) that is transparent to visible light (the holes are much larger (~ 1mm) than the wavelength of visible light (~.001 mm) -- the wavelength of microwave radiation (invisible light) is much greater (~100 mm)). Using these effective thicknesses, the fractional intensity of transmission can be calculated for cell phone frequencies (see below).The values in the above table have been adjusted to give the intensity of radiation at 5 cm from the oven (as per FCC regulations) -- the entry for 2.45 GHz reflects this (1 (or 5) mW/cm sq divided by 114 mW/cm sq). At 1.9 GHz (the frequency my cell phone uses), almost twice as much radiation is transmitted through the oven window than at 2.45 GHz (nearly ten times as much is transmitted at 0.9 GHz).

According to http://www.atttowers.com, I was just under a mile (5000 ft) from the nearest tower when I placed this call. If I assume that the broadcast power of my cell phone stayed the same when it was in the oven (it almost certainly increased), I can calculate how far that same call could have reached in the absence of the oven. Assuming a 1 mW/cm sq oven transmission, the call could have reached a tower nearly 8 miles away (5000 ft * sqrt(64.5)). This is a very reasonable distance (cell phones work in rural Sweden, afterall).

A cell phone will work inside of a microwave oven for two reasons:

1. They operate at different frequencies
2. Cell phones are designed to work under very poor conditions

On that note, if you're concerned about your cell phone, it almost certainly puts out more radiation when operated inside of a building (your phone compensates for poor reception by increasing broadcast power). So do us all a favor and take your call outside.

Conclusion
Based on the scattered data I've found, it's apparently safe to use a cell phone in the US (assuming you believe the SAR numbers, how the limits are established, and that SAR is the relevant figure of merit). If you're still worried, a hands-free headset (not positioned on your body) should be more than sufficient.

Assuming your oven isn't too leaky, microwave oven radiation is also well below established limits. I'm not saying that you should sleep on top of your oven, but the radiation it emits (which should only come out of the window) should be fairly week at few feet from the oven.

Miscellaneous Links
Here's some of the weirder stuff I found while researching this post:

People who volunteered to be microwaved
Disturbing naval research
Cook an egg hoax
Unscientific argument that microwave ovens will kill you
Unscientific argument that microwave ovens won't kill you

Copyright © 2009 Peter Dolph